Leapfrog integration of Omega Centauri's orbit in a Milky Way potential — pericentre passages, tidal stripping history, and cluster lifetime
| # | Time from now | r_peri | Mass after stripping |
|---|---|---|---|
| computing… | |||
The orbit is integrated using the leapfrog (Störmer-Verlet) algorithm with a 100 Myr timestep. The leapfrog is second-order symplectic, conserving a shadow Hamiltonian and showing only bounded energy oscillations over many orbital periods. For the ~150 Myr orbital period of OC this timestep is adequate for tracking pericentre passages; a 5 Myr step is used internally for the pericentre refinement pass.
A spherically-symmetric flat-rotation-curve potential is used: Φ(r) = V_c² ln(r) with V_c = 220 km/s. This reproduces the MW circular velocity at the solar radius (8.18 kpc) and gives an approximately correct orbital period and pericentre for OC. The full Allen-Santillan (1991) three-component potential (bulge + disk + NFW halo) would add ~10-15% corrections to pericentre distance and ~5% to orbital period; for a browser tool the flat-curve approximation is appropriate and clearly labeled as ⚠ model-dependent.
The reference Galactocentric position and velocity of OC are taken from Vasiliev & Baumgardt (2021), who derived proper motions from Gaia EDR3. The current Galactocentric distance of OC is 6.4 kpc. The velocity-scale slider multiplies the full 3D velocity vector by a constant factor, parameterizing uncertainty in the proper motion and the Galactic constants.
At each pericentre passage, a fraction f_strip of the remaining mass is removed: M → M × (1 − f_strip × (8 kpc / r_peri)²). The (8 kpc / r_peri)² term enhances stripping for closer passages, following the tidal force scaling. The initial mass is set to 4×10⁶ M☉ (present-day value from Baumgardt & Hilker 2018), and past pericentres are run backward in time, adding back stripped mass, to recover the mass budget. This is a simplified King-tidal estimate; N-body simulations show 1–5% mass loss per pericentre passage for typical OC orbits.
Dissolution is estimated by extrapolating the geometric mass-loss series (constant f_strip per peri) until M < 10% of the present-day 4×10⁶ M☉ value (i.e., < 4×10⁵ M☉). The extrapolation is geometric: after N_peri passages, M = M₀ × (1−f_eff)^N_peri where f_eff is the mean effective fractional loss per passage. This is a lower bound on longevity; dynamical friction, mass segregation, and external tidal shocks are not modeled here.